Find the quadratic polynomial, sum of whose zeroes is 5/2 and their pr

1.	Find the quadratic polynomial, sum of whose zeroes is 5/2 and their product is 1. Hence, find the zeroes of the polynomial.
Answer» Given : Sum of zeroes = (∝ + β) = 5/2 Product of the zeroes = = 1 Required quadratic polynomial is x² – (∝+β)x + ∝β = x² – (5/2)x + 1 = 1/2(2x² – 5x + 2) Now, find the zeroes of the above polynomial. Let f(x) = 1/2(2x² – 5x + 2) = 1/2(2x² – 4x – x + 2) = 1/2(2x(x – 2) – (x – 2)) = 1/2( (2x – 1)(x – 2) ) Substitute f(x) = 0. 1/2( (2x – 1)(x – 2) ) = 0 either (2x – 1) = 0 or (x – 2) = o x = 1/2 or x = 2 1/2 and 2 are the zeroes of the polynomial.

Find the quadratic polynomial, sum of whose zeroes is 5/2 and their product is 1. Hence, find the zeroes of the polynomial.

Answer»

Given : Sum of zeroes = (∝ + β) = 5/2

Product of the zeroes = = 1

Required quadratic polynomial is

x² – (∝+β)x + ∝β

= x² – (5/2)x + 1

= 1/2(2x² – 5x + 2)

Now, find the zeroes of the above polynomial.

Let f(x) = 1/2(2x² – 5x + 2)

= 1/2(2x² – 4x – x + 2)

= 1/2(2x(x – 2) – (x – 2))

= 1/2( (2x – 1)(x – 2) )

Substitute f(x) = 0.

1/2( (2x – 1)(x – 2) ) = 0

either (2x – 1) = 0 or (x – 2) = o

x = 1/2 or x = 2

1/2 and 2 are the zeroes of the polynomial.